$8$

$(8)$ Find a formula for the general term $\{a_n\}$ of the sequence $\{-1,\frac{2}{3},-\frac{1}{3},\frac{4}{27},$dots$\}$

$(9)($a$)$ Use the integral test to determine if the series converges. ${\displaystyle \underset{n=1}{\overset{}{}}}{n}^3{e}^{-n^4}.$

$($b$)$ Use the P$-$series test to determine if the series converges ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^{\sqrt[\phantom{2}]{2}}}$